A monotone interpolation method for the interpolation of ore size cumulative distribution in mineral processing industry

Abstract

Interpolation is a mathematical method to obtain new data points within the range of several known data points. The basic idea of interpolation is to construct a continuous function which passes through all the known data points so that new data points can be obtained from this function. In many practical problems, the interpolation function should be monotone due to physical meanings. However, nearly all of the classic interpolation methods, such as cubic spline interpolation, polynomial interpolation, etc. cannot ensure monotonicity. These methods therefore cannot be used to solve monotone interpolation problems. For this reason, monotone interpolation problems are presented separately from normal interpolation problems and corresponding monotone interpolation methods are required. In this paper, an interpolation framework named generalized mean Hermite interpolation framework which contains several renowned interpolation methods is developed and a monotone interpolation method based on this framework is proposed. It can be proved that among all the methods within the framework, the proposed method is the best one. The method is proposed for the interpolation problem of ore size cumulative distribution which is concerned in the simulation of mineral processing industry. It is an important problem because poor interpolation may lead to inaccurate simulation. However, despite of its importance, it is poorly done in nearly all of the existing mineral processing simulation softwares. Even JKSimMet, the most famous and widely used mineral processing simulation software in the world, cannot do a satisfactory job at this problem. Considering this, the proposed method is applied. Experiments show that its performance is much better than JKSimMet.